Question: Simplify the following expression: $y = \dfrac{10k^2 - 170k + 700}{k - 10} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ y =\dfrac{10(k^2 - 17k + 70)}{k - 10} $ Then we factor the remaining polynomial: $k^2 {-17}k + {70} $ ${-10} {-7} = {-17}$ ${-10} \times {-7} = {70}$ $ (k {-10}) (k {-7}) $ This gives us a factored expression: $\dfrac{10(k {-10}) (k {-7})}{k - 10}$ We can divide the numerator and denominator by $(k + 10)$ on condition that $k \neq 10$ Therefore $y = 10(k - 7); k \neq 10$